Case

UNIVERSITY OF JYVÄSKYLÄ

School of Business and Economics

WOULD STUDENT’S t-GARCH IMPROVE VaR ESTIMATES?

Master’s Thesis Spring 2005 Student: Abdelazim Reffat Mohamed Supervisor: Professor\ Juhani Raatikainen

UNIVERSITY OF JYVÄSKLÄ – SCHOOL OF BUSINESS AND ECONOMICS

Author: Abdelazim Reffat Mohamed Thesis title: Would student’s t-GARCH improve VaR estimates? Major subject: Economics Month and year: Spring 2005 Master’s thesis: 52 pages (including the cover pages)

ABSTRACT

In this study, GARCH volatility model was applied on Value at Risk methodology. The purpose is to compare between the performance of the plain GARCH (1,1) model that assumes normality of residuals, with the alternative student’s distribution GARCH (1,1) model within the VaR framework at the 95% confidence level. The two alternatives were empirically tested on a highly diversified portfolio consisting of two major European stock indices, The German stock index (DAX), and the French stock index (CAC). VaR estimates generated by each model were compared with actual P/L, and several backtesting techniques were applied to examine the validity of the two models. Both models generated identical VaR estimates with respect to number and distribution of exceptions. The two models were equally accepted by the tests of Kupiec (1995) and Christoffersen (1998). Lopez (1999) Loss function preferred normal GARCH since it slightly reduced the cost of exceptions, but an empirical comparison has shown that normal GARCH generally over stated the level of risk. Keeping in mind the equality of results from both models, and the associated opportunity cost if normal GARCH was chosen, t-GARCH model should be preferred.

Keywords: VaR, EWMA, GARCH, student’s t-distribution, backtesting.

Acknowledgments

This study has been carried out at the school of Business and Economics, University of Jyväskylä, Finland. I am very grateful to Professor Juhani Raatikainen in having provided me with the opportunity...